A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method. (English) Zbl 0598.65054

From authors’ summary: In part I [ibid. 11, 277-281 (1984; Zbl 0565.65041)] the authors gave a Noumerov-type method with minimal phase- lag for the integration of second order initial-value problems: \(y''=f(t,y)\), \(y(t_ 0)=y_ 0\), \(y'(t_ 0)=y_ 0'\). However, the method given there is implicit. We show here the interesting result that if the Noumerov-type methods of the paper mentioned above are made explicit with the help of the classical second order method, then there exists a selection of the free parameter for which the resulting method has a considerably small frequency distortion of size \((1/40320)H^ 6\) and also a (slightly) larger interval of periodicity of size 2.75 than the phase-lag of size \((1/12096)H^ 6\) and interval of periodicity of size 2.71 for the implicit method of the authors. More interestingly, it turns out that Noumerov made explicit of the first author [BIT 24, 117- 118 (1984; Zbl 0568.65042)] also has less frequency distortion than the (implicit) Noumerov method.
Reviewer: Z.Jackiewicz


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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[2] Chawla, M. M.; Rao, P. S., A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems, J. Comput. Appl. Maths., 11, 277-281 (1984) · Zbl 0565.65041
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